ABSTRACT. Using the data collected in a size selectivity experiment on Chilean hake (Merluccius gayi gayi) carried out in 2000, the selectivity parameters for four codend mesh sizes (100, 110, 130, and 140 mm of mesh size opening) were estimated and modelled by the SELECT model. These analyses included considerations of the sampling proportions of the catch in the codend and cover. Furthermore, the analyses took into account between-haul variation. The l50 values were 30.8, 29.9, 30.0, and 41.2 cm of total length, respectively, values lower than the estimates obtained from previous studies. The contribution of explanatory variables to the selectivity model was also tested in order to determine the role of mesh size, catch size (in number), and towing speed. Increases in catch size and in towing speed were accompanied by decreases in the l50 estimates. These results demonstrate how incorporation of subsampling effect and explanatory variables to model between-haul variation can improve selectivity estimates and management of a valuable resource.

Chilean hake (Merluccius gayi gayi) occurs along the coast of Chile between 23° and 47°S at depths from 50 to 500 m. It is the main demersal species caught along the central coast. The biomass of this resource decreased dramatically as a consequence of natural (cannibalism and predation) and fishing mortality from 2002 to 2005 and the current stock assessment indicates that it is overexploited (SUBPESCA, 2010). The proportion of fish below the size-at-maturity has increased since 2004 (more than 70% of the catches) and the present spawning biomass is below the limit reference level of 20% established for the fishery (SUBPESCA, 2010).

Regulation of mesh size is one of the most common management measures in fisheries. Specification and use of an appropriate mesh size can contribute to increases in the size of first capture and can reduce the mortality of smaller fish. Only one experiment on size selectivity has been performed for the Chilean hake trawling fishery over the last decade. Gálvez et al. (2000) analysed the selectivity of four mesh sizes (100, 110, 130 and 140 mm) using the covered codend method and the results were later published by Gálvez & Rebolledo (2005). These authors estimated similar l50 values among the different mesh sizes used, although the escape proportions increased with increasing mesh size. These results were compared with different selectivity studies carried out in Gadiformes (Fig. 1). A linear relation was found for this group of fishes between the mesh size and the 50% retention length, with a slope of ~0.4. Because Gálvez & Rebolledo (2005) found a lower value of the slope for this relationship (~0.1), the procedures were reviewed. In fact, the sampling proportions of the codend and cover were not considered in their analysis. Subsampling is necessary when the catch is so large that it is not possible to measure every single individual (Wileman et al., 1996). The effect of subsampling can be incorporated in two ways: (i) expanding the sample to the total catch or (ii) correcting the estimated parameters by a subsampling factor. Millar (1994) points out that the second case is preferable because it uses raw (unscaled) data and thereby ensures statistical rigour.

Replicate hauls using the same trawl and configuration indicate that codend

selectivity changes from one haul to another. Fryer (1991) indicated that the between-haul variation could be due to a number of "uncontrolled" factors. Examples of such factors include the haul duration, catch size, fishing season and depth among others (O'Neill & Kynoch, 1996; Millar & Fryer, 1999; Fonseca et al., 2007; Grimaldo et al., 2008; Sala & Lucchetti, 2010).

The objective of this study was to estimate the selectivity parameters so as to account for subsampling proportions. Moreover, explanatory variables were added in order to incorporate the effects of between-haul variation. The resulting parameter values were compared with previous estimates.

MATERIALS AND METHODS

Selectivity experiments were conducted during March-April 2000 on board a stern trawler (41.7 m overall length; 1900 HP) in the central-southern area of Chile (between 34°50'-35°40'S). Hauls were made during daylight hours at depths from 90 to 260 m. The duration of each haul varied between 14 and 135 min. Towing speed fluctuated between 3.0 and 4.0 knots (3.4 knots average speed) (Table 1). The hauls were carried out using a 53-m headline and 37-m footrope Engel Balloon Trawl, with four experimental codends of 100, 110, 130 and 140 mm mesh size opening. The covered codend method was used to retain the fish that escaped through the meshes (Galvez & Rebolledo, 2005). A length-frequency dataset was obtained from 32 covered codend experimental hauls (Table 1).

The data from each of the two compartments (codend and cover) were analysed separately. The catch weight for each compartment j was estimated for each haul. In order to estimate the catch in numbers of Chilean hake, a length-weight function was applied based on data recorded by Lillo et al. (2001). The average specimen weight was then determined (). The number of retained specimens by haul and compartment was obtained according to where Wj is the catch weight in each compartment.

For each haul, the retention probability r(l) of the codend was modelled using a logistic curve: , where r(l) is the (conditional) retention probability of a fish of length l given that it entered the codend (Wileman et al., 1996), and v = (ν1 + ν2)T is the vector of the selectivity parameters. The correction for the effects of subsampling was performed according to Millar (1994) who showed that for subsampled hauls , where ν1* = ν1 + ln(q) and is the rate of sampling proportions in the codend and cover, respectively. The selectivity parameters ν* and ν2 of the logistic curve were estimated by means of haul-by-haul maximum likelihood using the CC2000 software (ConStat).

The 50% retention length (l50) and the selection range (SR) were estimated as and , respectively. The model proposed by Fryer (1991) was then used to investigate the between-haul variation of the selectivity parameters ν1* and ν2 for each configuration, thereby allowing an average curve to be estimated for the codends. Analysis was done using the ECModel software (ConStat) based on the residual maximum likelihood (REML) method proposed by Fryer (1991). The individual contributions of various explanatory variables to the selectivity parameters were tested using the ECModel according to the REML method (Fryer, 1991). The variables considered were mesh size, catch (in number and weight), tow duration, depth and towing speed. The choice of the best fit model was based on the lowest value for Akaike's Information Criterion (AIC) (Fryer & Shepherd, 1996).

RESULTS

To calculate the sample weight in each compartment (codend and cover), the length-weight relationship wi = 7.76e -6li2.979 (R2=0.97) was used for both sexes. The catch in numbers for each haul was calculated using this relationship and the catch weight. The resulting values ranged between 437 and 37,345 specimens in the codend and between 83 and 10,507 in the cover (Table 1). The corresponding sample proportions (p1 and p2) varied between 0.005 and 0.185 in the codend and between 0.028 and 0.724 in the cover. Accordingly, the relationship between the sample proportions (q) ranged between 0.01 and 1.68 (=0.26). The q values for all hauls were taken into account in order to fit the selectivity models.

Fig. 2 shows the fitted curves for each haul. For all hauls, the estimated model resulted in good fits (P > 0.05) (Table 2). With the selection parameters ν1* and ν2 taken into consideration in the haul-by-haul analysis, the resulting estimates of l50 ranged between 26.4 and 35.6 cm for the 100 mm mesh; between 22.9 and 35.4 cm for the 110 mm mesh; between 23.7 and 34.0 cm for the 130 mm mesh and between 35.3 and 45.6 cm for the 140 mm mesh. Using the fit of the average curve based on between-haul variation, values of l50 were estimated as 30.8, 29.9, 30.0 and 41.2 cm for each mesh size, respectively (Table 2). Selection range (SR) tended to increase with increasing mesh size. However, the 130 mm mesh exhibited a value higher than expected from the general tendency observed. The average values of SR were 6.9, 7.2, 11.9 and 8.3 cm for the 100, 110, 130 and 140 mm meshes, respectively (Table 2).

Addition of the explanatory variables to account for between-haul variation indicated that the parameter ν1* depends significantly on the catch in numbers (P = 0.01) and the towing speed (P = 0.023), whereas ν2 depends on the mesh size (P < 0.001) (Table 3). This analysis yields a direct relation between l50 and the mesh size. On the other hand, the l50 value decreases as catch and towing speed increase. The model that best described selectivity was:

where ci is the catch (in numbers), si is the towing speed (knots) and mi is the mesh size (mm). The depth and duration variables did not contribute significantly to the model.

The effect of the catch for each mesh size used in the model was analysed for a range of 1,000 to 35,000 specimens caught and for a fixed towing speed corresponding to the average value of 3.4 knots. A significant decrease of at least 6 cm TL in the l50 value for extreme catches was observed for all mesh sizes (Fig. 3). For example, the l50 of the 100 mm mesh was 29.9 cm for a small catch (1,000 specimens), while this value decreases to 23.1 cm for a large catch (35,000 specimens).

Likewise, the model with towing speeds between 3 and 4 knots was evaluated assuming a constant catch of 10,000 individuals. A decrease of at least 4.5 cm TL in the l50 value for extreme speeds was observed (Fig. 4). For the 140 mm mesh at a towing speed of 3 knots, the l50 was 39.0 cm. This value decreased to 33.1 cm for a towing speed of 4 knots.

Note that ν2 depends only on the mesh size. Accordingly, the SR values estimated using the model were 7.2, 7.7, 8.9 and 9.6 cm for the meshes of 100, 110, 130 and 140 mm, respectively.

DISCUSSION

This study was based on the same data used by Gálvez & Rebolledo (2005). However, the results of the two studies differ (Fig. 5). The main analytic difference is that these authors assume that the sampling proportions in the codend and in the cover are equal. This assumption leads to a significant overestimation of the selectivity parameters. When this effect and the between-haul variation are both taken into account, the l50 estimate decreased by 9 cm for the 100, 110 and 130 mm mesh. The difference is lower (~4 cm) in the 140 mm mesh (Fig. 5).

Incorporation of subsampling effects produced a high dispersion of the l50 values. This effect is the result of other variables included in the selection process. This consideration led us to introduce explanatory variables to the model and by including the mesh size, the catch (in numbers) and the towing speed, it was possible to achieve significant reductions in the dispersion of the estimates (Fig. 5). The effect of catch size on codend selectivity has been discussed in numerous studies. Some authors find that increasing catch size reduces l50 (Ehrhardt et al., 1996; Erickson et al., 1996; Tschernij & Holst, 1999; Madsen et al., 2002; Grimaldo et al., 2007). However, others have obtained the opposite result (O'Neill & Kynoch, 1996; Dahm et al., 2002), while emphasising that selectivity tends to decrease when the catch size is very high. On the other hand, the studies of Madsen et al. (1998), O'Neill et al. (2006) and Grimaldo et al. (2008) yielded inconclusive results or found only a weak effect of the catch variable.

Many different factors are involved in gear selectivity. For example, alterations in and obstruct-tions of the escape channels can be produced, and changes can also occur in the tension-deformation relation of the meshes. Indeed, Erickson et al. (1996) point out that large catch sizes can obstruct the codend meshes and thereby reduce the potential escape channels for fish. Additionally, in some Gadidae, haddock and whiting for example, "opportunistic escape" is more common than "active escape" (Jones et al., 2008). This difference results in a reduced probability of escape as the catch size increases. Tension-deformation is also an important factor. The increased size of the mesh opening and the change in the shape of the codend would both favour increased selectivity (O'Neill & Kynoch, 1996; Herrmann, 2005; Madsen, 2007). Nevertheless, the increased drag produced by the operation of the trawl can increase the tension on the mesh bars. This increased tension can make escape more difficult (O'Neill et al., 2005) or can injure fish, thereby conditioning their post-escape survival (Suuronen, 2005).

Increased trawl speed thus affects selectivity adversely for two different reasons. Increased speed increases the resistance encountered by the gear, raises the tension on the codend meshes, and consequently reduces the mesh opening (Dahm et al., 2002; O'Neill et al., 2005). On the other hand, an increase in trawl speed also reduces the swimming performance of fish (Dahm et al., 2002; Breen et al., 2004). In this study, we did not have enough information to identify a particular mechanism responsible for the l50 decrease. However, Queirolo et al. (2010) noted in hake that when fish are close to the codend at a towing speed of 4 knots, most fish exhibit no movement, appear exhausted and drop back into the codend.

The model obtained in this study indicates that the selectivity decreases as the catch size increases. This effect could be explained by the obstruction of the escape channels and by the closure of the meshes due to the increase of the tension. In the model, selectivity also decreased with increased towing speed. This effect can be attributed to the lower swimming performance of the fish. The significance found for the explanatory variables in the selectivity model indicates that these variables could be included in management "good practices" recommendations for users. Although the tow duration was not significant in our results, we recognize that this variable plays an important role both during the escape phase and postescape survival (Suuronen, 2005), so it should be consider in subsequent studies.

In order to reduce the juvenile catch and avoid growth overfishing, the recommended value of l50 should be greater than or equal to the size at sexual maturity estimated as 34 cm TL by Lillo et al. (2009). Likewise, assuming an average catch of 10,000 fish and an average towing speed of 3.4 knots, an estimate of the minimum mesh size recommended for the fishery is 125 mm. However, at present, the use of 100 mm mesh and a 90-mm square mesh panel are mandatory (see Queirolo et al., 2008). For this reason, it is fundamental to evaluate and compare the whole selectivity of these codends for the fishery. These recommendations demonstrate ways in which the addition of the subsampling effect and the use of explanatory variables to model between-haul variation can allow fisheries scientists to improve selectivity estimates for Chilean hake.

ACKNOWLEDGEMENTS

We thank the Fondo de Investigación Pesquera (FIP) for authorising this reanalysis of the data and for facilitating access to the databases of the FIP 96-25 project. Special thanks to the Centro Andaluz de Ciencia y Tecnología Marinas (CACYTMAR) for logistical support and anonymous reviewers for their valuable comments. Dante Queirolo also thanks the Comisión Nacional de Investigación Científica y Tecnológica (CONICYT, Programa Becas Chile) for the fellowship awarded.